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Chapter 38: Performance Measurement: Plus Alpha vs. Transfer Pricing

Chapter 38: Performance Measurement: Plus Alpha vs. Transfer Pricing

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PORTFOLIO STRATEGY AND RISK MANAGEMENT



TRANSACTION-LEVEL PERFORMANCE MEASUREMENT VS.

PORTFOLIO-LEVEL PERFORMANCE MEASUREMENT

There is a central tenet of performance management that we need to keep in mind for

the rest of this chapter:

A performance measurement system which sends incorrect signals at the

transaction level will be inaccurate at the portfolio level as well, since the

portfolio is the sum of its individual transactions.

In Chapters 2 and in van Deventer and Imai (2003), buy low/sell high was

outlined as the ultimate transaction-level guide to asset and liability selection. If an

asset worth 102 can be purchased at a cost of 100, we should do it. If another asset

worth 101 can be purchased at a cost of 100, we should buy that, too. What could be

simpler than that? This basic performance measurement system has been at the heart

of capitalism for thousands of years, and our objective in this chapter is to strip back

some of the institutional baggage of financial institutions’ performance measurement

systems to reveal performance as clearly as these examples.

In Chapters 19 through 35, we showed that every single type of asset and liability

issued by major financial institutions can be valued precisely both before the asset or

liability is added to the balance sheet and every instant thereafter. We now know enough

to do the simple assessment in the previous paragraph. Are there any real or imagined

complexities that may complicate the buy low/sell high transaction-level performance

assessment? There are only a few and we mention them briefly in this section:

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Costs of origination may have both a large fixed cost component and a marginal

cost component, which impact our assessment of buy low/sell high. A classic

example is the consumer deposit gathering franchise of a commercial bank. On

the transaction level, a 90-day consumer certificate of deposit may cost 25 basis

points less than a wholesale certificate of deposit (CD) with the identical

maturity. Based on this information alone, the first-pass buy low/sell high

decision is buy—originate the retail CD. The costs of origination and servicing

need to be included in the analysis for a complete answer. What if there was a $1

per month fixed cost of servicing the consumer CD that would not impact the

wholesale CD? We just need to add this to the effective cost of the retail CD to

have a more accurate answer. More realistically, the head of the retail banking

division should be constantly re-evaluating this calculation: I can sell the

building housing my River City branch for $500,000 today. Or I can keep it, pay

staff expenses of $450,000 per year, and issue a large number of consumer CDs.

Which is better? This is still a buy low/sell high calculation that requires no

capital allocation to do correctly. It is a question that should be continually

asked. A related question is whether the 25 basis point margin on the consumer

CD is the margin that produces maximum present value (that marginal revenue

equals marginal cost from basic economic theory is relevant here). There are

other calculations that come into play that we mention next.

Future business may depend on doing current business, with an actuarially likely

arrival of good buy low/sell high business going forward. The example above is a

good example to illustrate another complexity in assessing performance of any



Performance Measurement



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business. The River City branch’s existence may give us the real option to do lots

of retail CD business going forward. This retail business depends both on our

pricing and our own default probability as we saw in Chapter 37 on liquidity

risk. The probability of a client rolling over one profitable retail CD has characteristics that are very similar to that of the reduced form credit models we

discussed in Chapter 16, the credit default swaps we discussed in Chapter 20,

and the insurance policies we valued in Chapter 35. Doing a really good buy

low/sell high decision analysis depends on taking these facts into account in a

careful way. It has nothing to do with capital allocation—it’s a straightforward

net present value calculation using the analytics presented in Chapters 19 to 35.

Some costs may be shared with other products. What if the River City branch

also makes profitable small business loans (valued correctly using the technology

of Chapter 19 and 20), and that there is a fixed cost of monitoring them that is in

part embedded in the $450,000 staff costs of the River City branch? Again,

assessing whether to close the branch or keep it and optimize pricing is a riskadjusted present value calculation like those in Chapters 19 through 35—shared

fixed costs simply broaden the boundaries of the calculation that has to be done

and the transactions that have to be included. Capital allocation is again irrelevant. What is relevant is the available market return that has the same risk as

keeping the River City branch open.

Cash might be tight. Van Deventer and Imai (2003) discuss how the buy low/sell

high transaction-level performance measurement strategy has to be tempered by

the financial institution’s ability to buy low. Chapter 37 discusses how, as a

financial institution’s risk rises, the supply of funds to the financial institution can

fall or reach zero. At such a high level of risk, the financial institution has lost its

real option to buy low/sell high. This is one of the reasons why financial institutions

typically find that their optimal credit risk from a shareholder value-added perspective is consistent with default probabilities in a low range, a lesson they learned

the hard way in the 2006–2011 credit crisis. We deal with this issue in more detail

in the next chapter. This “own default risk” issue is why the buy low/sell high

performance measurement test outlined previously is necessary, but not sufficient,

to result in the origination of an asset or liability. The financial institution’s own

default risk impacts its ability to exercise its option to buy low/sell high.



The preceding examples show that, even at the transaction level, portfolio

considerations can be important. The decision to issue retail CDs depends on the

total volume that can be done (the portfolio of CDs), not just the pricing on one CD.

The decision on whether to keep or sell the branch depends on transaction level

benefits of the retail CD and small business loan portfolio transactions at the branch.

Finally, the decision to buy low/sell high can depend on the entire existing portfolio

of assets and liabilities, since they determine the current credit risk of the institution.



PLUS ALPHA BENCHMARK PERFORMANCE VS. TRANSFER PRICING

In Chapter 2, we discussed both the financial accounting–oriented transfer pricing

system used by commercial banks and the market value–based benchmark performance system used by almost every other type of financial institution. The authors



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PORTFOLIO STRATEGY AND RISK MANAGEMENT



believe that commercial banks would benefit from adopting the benchmark-based

performance measurement approach, while being careful to avoid the pitfalls of such

an approach as outlined in Chapter 2.



WHY DEFAULT RISK IS CRITICAL IN PERFORMANCE MEASUREMENT

OF EQUITY PORTFOLIOS

The risk management techniques in common use for equity portfolio management

include Nobel prize–winning concepts such as the capital asset–pricing model

(CAPM), arbitrage pricing theory (APT), and the efficient frontier concept. The list of

researchers behind these concepts reads like a who’s who of finance: William Sharpe,

Harry Markowitz, John V. Lintner, Jr., Jan Mossin, Steven Ross, and many other key

contributors. Like any theory, however, the CAPM, APT, and efficient portfolio

concept are based on the same flaw that has doomed simple implementations of

value-at-risk (VaR) and the copula approach for CDO valuation: a normal distribution of equity returns is at the heart of CAPM, APT, and the efficient frontier.

Default risk is ignored. The current credit crisis makes a more sophisticated and

realistic assessment of risk in equity portfolios a mission critical function. We discuss

how to do that in this section.

In our discussion of value at risk in Chapter 36, we observed that the assumption

that equity returns are normally distributed with their historical mean and standard

deviation is so highly stylized that it makes default disappear like magic. In Bear

Stearns’ case, for example, the historical mean and variance of monthly returns from

January 1990 onward implied that the probability of a À100 percent return in a

given month was zero to six decimal places. The fact that this À100 percent return

did occur is not a “black Swan” á la Nassim Taleb; it is a very predictable result that

is a measurable probability for any public firm. The decision to ignore default in

measuring risk and return in equities is a simplification that has proven extraordinarily costly to many in the 2006–2011 credit crisis. Still we hear things like this all

the time from equity portfolio managers:

Why do I need default probabilities? I manage an equity portfolio, not a

fixed income portfolio.

On hearing this, John Y. Campbell of Harvard University laughingly responded,

“Don’t they know that equity is the most highly subordinated liability on the balance

sheet of a public firm?” He’s exactly right. A more subtle argument for ignoring

default in equity portfolio management is embedded in this comment:

I don’t need default probabilities to manage my equity portfolio. My

benchmark is the S&P 500 and no firm in the S&P 500 has ever defaulted.

It turns out, thanks to the Standard & Poor’s website, that this comment is

dramatically untrue. Remember Dana Corporation? Calpine? Delphi? Winn-Dixie?

All of these firms failed while they were a component of the S&P 500. There is a more

important phenomenon, however, that is very much credit driven that affects equity

managers. Consider firms like Washington Mutual, Wachovia, Merrill Lynch,



Performance Measurement



769



General Growth Properties, and Lehman Brothers. All of them were thrown out of the

S&P 500 as their credit quality deteriorated. These changes in the composition in

the index happen “after hours.” The stock price of the firm dropped from the index

will be down 10 to 20 percent at the next day’s open, and the stock price of the firm

replacing them in the index will be up 10 to 15 percent on the open. Even if the equity

portfolio manager is running a perfect replica of the S&P 500, the manager will lose

the equivalent of 20 percent (best case) to 35 percent on one of the 500 elements of the

index because of this phenomenon. This is a serious “negative alpha” phenomenon.

Changes in index composition are similar to what the always insightful Michael Lewis

(2004) pointed out in his baseball book Money Ball: walking is a skill, not an accident.

Similarly, changes in index composition are not accidents either. They are highly

predictable, and the default probabilities of the companies in the index have a very

high degree of correlation with their probability of being dropped from the index.

Just as important to equity managers is the disconnect between the credit default

swap market and equity returns. The CDS market is focused on senior unsecured

debt. What if Citigroup is bailed out continuously but not nationalized? Most

observers expect that equity holders will lose everything (by being completely diluted)

and debt holders will lose nothing. Only default probabilities that predict the

probability of the company failing (i.e., the shareholders being wiped out) capture

this impact correctly. The CDS quotes for this example, Citi, would be much lower

than the correct default probabilities because they reflect anticipation of 100 percent

recovery like that which has accompanied the creeping nationalization of AIG.



“PLUS ALPHA” PERFORMANCE MEASUREMENT IN

INSURANCE AND BANKING

With the proper adjustments discussed in the prior section, the comparison of actual

mark-to-market performance relative to a naïve index of the same risk is a highly

useful and very simple concept. The only trick in implementing this approach in the

commercial banking and insurance arena is the need to create benchmarks. For

example, as van Deventer and Imai (2003) suggest, the head of retail banking who

owns the three-year auto loan portfolio should be judged by the market value of a

U.S. Treasury index that replicates the exact cash flow timing and amount of each

auto loan on a full option-adjusted basis. We show in Chapter 40 that this is a

modest computer science effort that is already commercially available and it is merely

a question of institutional will to move in this direction.

The manager of the three-year auto loan portfolio is a good performer if over

time the mark-to-market value of the auto loans, after expenses and after actual

credit losses, is a larger number than the mark-to-market value of the artificial

Treasury auto loan index.

The manager of the auto loan portfolio will use transaction-level analytics to decide

which loans to originate and which loans to pass on. An important part of this relates

directly to the reduced form modeling technology we discussed in Chapters 16 and 17:

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The default probability of each auto loan borrower has to be correctly assessed

using state-of-the-art logistic regression such as that discussed in the public firm

default probability context in Chapter 16.



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PORTFOLIO STRATEGY AND RISK MANAGEMENT



The proper credit spread for the auto loan has to be assessed in light of expenses

of origination and monitoring and in conjunction with the macro factors driving

default. In addition, the probability of prepayment has to be taken into account

as discussed in Chapters 27 to 29.

Once breakeven pricing is set for each borrower, the bank can accept or reject

the loan. Skillful loan selection creates plus alpha performance at the portfolio

level by creating value one loan at a time.



This is true buy low/sell high implementation, consistent with state-of-the-art

state of the art credit risk and interest rate risk management. A benchmark performance that is plus alpha will show management exactly how much value has been

created by this business above and beyond what would have been achieved by a

matched maturity investment in U.S. Treasury securities with identical payment dates,

payment amounts, and options characteristics. Of course the more traditional transfer

pricing methodology used in commercial banking can be used to show this as well, but

the transfer pricing yield curve will be the U.S. Treasury yield curve, not the marginal

cost of funds yield curve of the bank. In addition, the transfer pricing rate will include

a premium that reflects the prepayment option held by the auto loan borrower.



DECOMPOSING THE REASONS FOR PLUS OR MINUS ALPHA IN A FIXED

INCOME PORTFOLIO

One of the most interesting set of cultural differences we have come across in finance

is the difference between investment managers and bankers. One could write 100

books and 2 million jokes about those differences, but this section has a more modest

ambition: to show how to improve fixed income performance attribution in both

investment management and in banking by combining best practice from both types

of institutions. This section is an introduction to that topic.

We can briefly summarize the key causes of the cultural differences between fixed

income investment managers and bankers in a few bullet points:

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Nature of assets managed: The overwhelming majority of the assets held by fixed

income fund managers is publicly traded. The overwhelming majority of assets

held by banks, at least by number of transactions, is not publicly traded.

Nature of performance measurement: In fixed income fund management, performance measurement is based on market valuation and both absolute returns

and returns versus a benchmark portfolio. In spite of more than 40 years of debate

in banking, that industry remains largely driven by financial accounting–based

performance measurement, not market value–based performance measurement.

Granularity of performance measurement: The CFA Institute, formerly known

as the Association for Investment Management and Research, has long recommended calculating performance using daily time periods. Outside of the trading

floor, banks are largely driven by monthly or quarterly time frames.

Volume of transactions: Most investment managers would have no more than

5,000 or 10,000 positions, and many would have far less. One of the world’s

five largest banks has more than 700 million distinct assets and liabilities. This

creates a much bigger information technology footprint in banking by necessity.



Performance Measurement

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Staff count: Staffing in investment management is lean and mean, because very

little retail business is done, at least relative to banking. The largest banks in

North America, by contrast, have a staff count in the hundreds of thousands.

Analytical rigor: There are brilliant people in both banking and fixed income

investment management who are well beyond best practice in their analysis.

That being said, it is much more tempting to manage risk with a spreadsheet or

risk analysis that is not much more powerful than a spreadsheet when the

portfolio has a relatively small transaction count, something very common in

the hedge fund industry in particular.



We recently came across a European paper on fixed income performance attribution that relied heavily on standard yield-to-maturity calculations and duration as

the basis for improved fixed income performance attribution. The purpose of this

section, in an introductory way, is to explain why it is particularly important in fixed

income portfolio attribution to apply much more accurate and modern techniques

than the duration concept, because the errors embedded in the yield-to-maturity

concept and duration (as we discussed in Chapter 4) are large and can result in wildly

inaccurate assessments of fixed income performance attribution:

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Yield-to-maturity discounts cash flows at all payment dates at the same interest

rate

If the same issuer has two bonds outstanding with different yields to maturity,

interest payments on the same dates will be discounted at different rates for each

bond

Common spread calculations are usually the simple difference between the yields

to maturity on two bonds with similar but not identical maturity dates



Now we can see the benefits of cross-pollenization of risk management between

bankers and fixed income fund managers:

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We take the mark-to-market orientation of fund managers.

We take the exact day count matched maturity transfer pricing concept from

banking.

We take the yield curve smoothing concepts that are essential to transfer pricing

in banking.

We take the macroeconomic factor–driven stress testing approach from banking

and bank regulators that has come out of the 2006–2011 credit crisis.

We then use this technology to analyze the reasons for mark-to-market performance changes in a way already familiar to fixed income fund managers but

with greater accuracy.



We know that changes in a large number of macroeconomic factors affect performance of fixed income portfolios. A small sample of them is listed here:

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Level and shape of the risk-free yield curve

Home prices

Commercial real estate prices

Oil prices



772

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PORTFOLIO STRATEGY AND RISK MANAGEMENT



Other commodity prices

Foreign exchange rates

Market volatility

Unemployment rates

Changes in real gross domestic product

Government surpluses or deficits



Best practice risk managers are increasingly measuring the impact of each of

these factors on mark-to-market performance by tracing their impact on credit

spreads, prepayment, and default risk of borrowers from retail to small business to

major corporations to sovereigns. In the example of this section, we keep it simple.

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We analyze the performance of one bond

We assume that we only need to analyze three drivers of performance:

(1) changes in the risk-free yield curve and (2) the credit spread for the bond

issuer, along with (3) the passage of time.

We look from the perspective of July 15, 2010, and ask the question, “How

much did these risk factor movements contribute to the gain or loss in the value

of our bond since April 15, 2010?” We could just as easily do the analysis for a

portfolio versus a benchmark. We keep it very simple here for expository

purposes.



A more complete analysis has a much longer list of drivers of performance that

includes all of the macro factors above plus many more.



A WORKED EXAMPLE OF MODERN FIXED INCOME

PERFORMANCE ATTRIBUTION

We now go through a worked example of a more modern approach to fixed income

performance attribution with one bond issued by ABC Company and three drivers of

performance: the risk-free yield curve, the spread, and the passage of time.

We assume the ABC bond has a par value of 1,000, a 10 percent coupon,

semiannual coupon payment dates of June 30 and December 31, and a maturity on

June 30, 2019. We observe in the marketplace these prices:

April 15, 2010: $1532.60 (net present value ¼ price plus accrued interest)

July 15, 2010: $1580.18

We ask this question: What factors have caused the net present value of the bond

to change from $1532.60 to $1580.18? How much was due to the passage of time,

how much to changes in the risk-free rate, and how much to spread changes?

We answer this question by using the maximum smoothness forward rate

approach to yield curve smoothing outlined in Chapter 5. We apply these techniques

to the risk-free yield curve and to the ABC bonds outstanding to derive a risk-free and

risky yield curve on April 15, 2010, and July 15, 2010. As a substitute for a risky

yield curve derived from all ABC bonds outstanding, we assume that, by coincidence,

the yield curve for ABC is identical to the U.S. dollar LIBOR-swap curve.



773



Performance Measurement



For example, Exhibit 38.1 shows the zero-coupon bond yields for the risk-free

and risky (ABC curve or swap curve) on April 15, 2010, as reported in Kamakura’s

“Friday Forecast.”1

Note that, on this day, the risk-free yield curve’s zero-coupon yields were actually higher than the ABC Company/swap curve zero yields at the longer maturities.

This is an increasingly common phenomenon that recognizes that the risk-free or

sovereign yield curve is not, in fact, risk free.

In Exhibit 38.2, we also take the zero-coupon yields for the risk-free and risky

ABC/swap yield curve on July 15, 2010.

Over this three-month period, we can see that the risk-free, zero-coupon yield

curve has fallen substantially as shown in Exhibit 38.3.

Risky zero-coupon yields, with the exception of the short maturities, have also

moved downward, as this graph in Exhibit 38.4 shows.

The zero-coupon credit spread for ABC company/swap curve has moved as

shown in Exhibit 38.5.

Many researchers have found that it is common for credit spreads to rise when

risk-free yields fall, and that is consistent with yield curve movements between these

two dates. We extract the following zero-coupon bond prices from both yield curves

on both dates and apply it for performance attribution to the cash flows on the ABC

bond as shown in Exhibit 38.6.



6.00000



5.00000



Percent



4.00000



3.00000



2.00000



1.00000



0.000

0.667

1.333

2.000

2.667

3.333

4.000

4.667

5.333

6.000

6.667

7.333

8.000

8.667

9.333

10.000

10.667

11.333

12.000

12.667

13.333

14.000

14.667

15.333

16.000

16.667

17.333

18.000

18.667

19.333

20.000

20.667

21.333

22.000

22.667

23.333

24.000

24.667

25.333

26.000

26.667

27.333

28.000

28.667

29.333

30.000



0.00000



Years to Maturity

Risk-Free Yield from Quartic f with f "(0) ϭ 0, f "(T)=0 and f '(T) ϭ 0 from bond prices



Swap Zero-Coupon Yield



EXHIBIT 38.1 U.S. Treasury and USD Interest Rate Swap Zero-Coupon Yields Derived from

the Federal Reserve H15 Statistical Release Using Maximum Smoothness Forward Rate

Smoothing, April 15, 2010

Sources: Kamakura Corporation; Federal Reserve.



PORTFOLIO STRATEGY AND RISK MANAGEMENT



774

4.50000

4.00000

3.50000



Percent



3.00000

2.50000

2.00000

1.50000

1.00000

0.50000



0.000

0.667

1.333

2.000

2.667

3.333

4.000

4.667

5.333

6.000

6.667

7.333

8.000

8.667

9.333

10.000

10.667

11.333

12.000

12.667

13.333

14.000

14.667

15.333

16.000

16.667

17.333

18.000

18.667

19.333

20.000

20.667

21.333

22.000

22.667

23.333

24.000

24.667

25.333

26.000

26.667

27.333

28.000

28.667

29.333

30.000



0.00000



Years to Maturity

Risk-Free Yield from Quartic f with f "(0) ϭ 0, f "(T) ϭ 0 and f'(T) ϭ 0 from bond prices



Swap Zero-Coupon Yield



EXHIBIT 38.2 U.S. Treasury and USD Interest Rate Swap Zero-Coupon Yields Derived from

the Federal Reserve H15 Statistical Release Using Maximum Smoothness Forward Rate

Smoothing, July 15, 2010



4.500%

4/15/2010 Risk-Free Zero-Coupon Yield

7/15/2010 Risk-Free Zero-Coupon Yield



4.000%

3.500%



Percent



3.000%

2.500%

2.000%

1.500%

1.000%

0.500%



Maturity Date



EXHIBIT 38.3 Risk-Free, Zero-Coupon Yields, April 15, 2010, and July 15, 2010



20190430



20181031



20180430



20171031



20170430



20161031



20160430



20151031



20150430



20141031



20140430



20131031



20130430



20121031



20120430



20111031



20110430



20101031



20100430



0.000%



775



Performance Measurement

4.500%

4/15/2010 Risky Zero-Coupon Yield

4.000%



7/15/2010 Risky Zero-Coupon Yield



3.500%



Percent



3.000%

2.500%

2.000%

1.500%

1.000%

0.500%



20190430



20181031



20180430



20171031



20170430



20161031



20160430



20151031



20150430



20141031



20140430



20131031



20130430



20121031



20120430



20111031



20110430



20101031



20100430



0.000%



Maturity Date



EXHIBIT 38.4 Risky Zero-Coupon Yields, April 15, 2010, and July 15, 2010

0.600%

4/15/2010 Zero-Coupon Credit Spread

7/15/2010 Zero-Coupon Credit Spread



0.500%



Percent



0.400%



0.300%



0.200%



0.100%



Maturity Date



EXHIBIT 38.5 Zero-Coupon Spreads, April 15, 2010, and July 15, 2010



20190430



20181031



20180430



20171031



20170430



20161031



20160430



20151031



20150430



20141031



20140430



20131031



20130430



20121031



20120430



20111031



20110430



20101031



0.100%



20100430



0.000%



EXHIBIT 38.6 Actual Zero-Coupon Yields and Zero-Coupon Credit Spreads



Date

20100430

20100531

20100630

20101231

20110630

20111231

20120630

20121231

20130630

20131231

20140630

20141231

20150630

20151231

20160630

20161231

20170630

20171231

20180630

20181231

20190630



776



4/15/2010

Risk-Free,

ZeroCoupon

Yield



4/15/2010

Risky

ZeroCoupon

Yield



4/15/2010

ZeroCoupon

Credit

Spread



7/15/2010

Risk-Free

ZeroCoupon

Yield



7/15/2010

Risky

ZeroCoupon

Yield



7/15/2010

ZeroCoupon

Credit

Spread



Change

in RiskFree Zero

Yields



Change

in Risky

Zero

Yields



Change

in Zero

Spreads



0.163%

0.160%

0.159%

0.310%

0.537%

0.850%

1.171%

1.468%

1.737%

1.995%

2.239%

2.476%

2.697%

2.908%

3.099%

3.274%

3.427%

3.564%

3.682%

3.788%

3.879%



0.279%

0.358%

0.394%

0.488%

0.651%

0.974%

1.321%

1.633%

1.910%

2.175%

2.420%

2.648%

2.848%

3.025%

3.177%

3.312%

3.431%

3.539%

3.638%

3.731%

3.817%



0.116%

0.198%

0.235%

0.178%

0.114%

0.124%

0.149%

0.165%

0.174%

0.180%

0.180%

0.172%

0.150%

0.117%

0.079%

0.039%

0.004%

À0.024%

À0.044%

À0.056%

À0.062%



0.193%

0.264%

0.394%

0.593%

0.787%

0.967%

1.155%

1.352%

1.560%

1.763%

1.963%

2.149%

2.321%

2.474%

2.613%

2.733%

2.842%

2.936%



0.729%

0.631%

0.641%

0.850%

1.048%

1.217%

1.407%

1.611%

1.813%

1.995%

2.163%

2.312%

2.448%

2.568%

2.677%

2.775%

2.864%

2.945%



0.535%

0.367%

0.247%

0.257%

0.261%

0.250%

0.252%

0.259%

0.253%

0.232%

0.200%

0.163%

0.127%

0.093%

0.065%

0.041%

0.023%

0.009%



À0.025%

À0.147%

À0.293%

À0.420%

À0.536%

À0.637%

À0.712%

À0.766%

À0.800%

À0.825%

À0.841%

À0.856%

À0.867%

À0.878%

À0.885%

À0.891%

À0.895%

À0.898%



0.280%

0.085%

À0.159%

À0.300%

À0.434%

À0.557%

À0.637%

À0.688%

À0.724%

À0.755%

À0.776%

À0.791%

À0.799%

À0.805%

À0.809%

À0.815%

À0.821%

À0.829%



0.305%

0.232%

0.134%

0.120%

0.102%

0.080%

0.075%

0.078%

0.076%

0.070%

0.065%

0.065%

0.068%

0.073%

0.076%

0.077%

0.074%

0.069%



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Chapter 38: Performance Measurement: Plus Alpha vs. Transfer Pricing

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